I love thinking about that possibility! Because we scifi writers tend to create worlds that are far superior in technological progress than even the so-called magic that is featured in Harry Potter. Even Harry's battles with Voldemort can be compared to Luke's battles with Vader, Harry Potter vs. Star Wars and a whole bunch of other things in the novel are very, very comparable to Star Wars itself or at least other elements in sci-fi.They don't appear to need or want computers, though computers are probably more efficient than some of their magic. But even though the magic in the Harry Potter world is very cool, I think our technology will fast surpass it. Magic appears stagnant. The popularity of many spells and charms comes and goes, and I'm sure combinations have always varied for differing results. But we do not see evidence that magic truly develops the way technology does.
For instance, Hogwarts is an incredibly complex magical building created a thousand years ago. The Ministry of Magic is also old. Even though adaptations are sometimes made, we don't see "improvements" in the technology/magic used for more modern buildings. Witches/wizards rode broomsticks hundreds of years ago. They still ride broomsticks today. We walked or hode horses hundreds of years ago. Today we fly in airplanes - far superior to broomsticks.
But the muggle world makes technological advances very quickly. What happens to the magical world when muggle technology completely leaves it behind?
I think we all have those dreams about Arithmancy, but JK revealed it is about forecasting and not much complex maths is involved.In the HP World, Magic is not Stagnant. I forget the guys name, but one of the members of Prof Slughorn's "Slug Club" is mostly there because his Uncle invented a new kind of potion. Not to mention the Snape's "Half Blood Prince" Potions book, in which he appears to have invented a couple of new spells.
I notice the most obvious way that Wizards use to get around not having Computers has not even been mentioned!! Hermione of course, takes "Arithmancy" lessons, which sounds like some sort of magic based system for making complex calculations and so on.
I'm with you.Me and my brother have always had an argument about magical worlds - his position is that technology simply cannot exist beyond medieval era in a world with magic